Pyrorectichoron (EntityTopic, 11)

From Hi.gher. Space

The pyrorectichoron is a uniform polychoron in the pyrotope family. Its cells are 5 tetrahedra and 5 octahedra.

The pyrorectichoron can be constructed as tetrahedron || octahedron, meaning it's also a segmentochoron, K4.5. Deleting any vertex from the pyrorectichoron forms the trigonal biantiprismatic ring, or K4.6, which can be constructed as trigonal prism || gyrated triangle. Deleting another vertex - specifically, one of the three from the gyrated triangle - will form the digonal gyrobicupolic ring, or K4.8.


The following Petrie polygon and stereographic projection each highlight the same arrangement of two neighboring (at a point) tetrahedral cells in red and orange and the octahedral cell between them in blue:

(image) (image)

In the Petrie polygon, as there are a total of 5 tetrahedra and 5 octahedra, the others can be obtained by rotating the above highlights by τ5.

Incidence matrix

Dual: (dual of pyrorectichoron)

0 Va = point ;
1 Ea 2 = digon ;
2 3a 33 = triangle ; tet-oct
3 3b 33 = triangle ; oct-oct
4 C1a 4640 = tetrahedron ;
5 C2a 61244 = octahedron ;
6 H4.1a 1030201055 = pyrorectichoron ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.

Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus